Report of the Annual Meeting [article]

1920 Proceedings of the National Academy of Sciences of the United States of America  
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more » ... out Early Journal Content at JSTOR is a digital library of academic journals, books, and primary source objects. JSTOR helps people discover, use, and build upon a wide range of content through a powerful research and teaching platform, and preserves this content for future generations. JSTOR is part of ITHAKA, a not--for--profit organization that also includes Ithaka S+R and Portico. For more information about JSTOR, please contact 442 REPORT OF THE ANNUAL MEETING PROC. N. A. S.. The paper discusses the effect of the neglect 6f these conditions and a more general treatment, as an extension of the original treatment by Joukovsky, is then developed for taking care of conditions (1), (2), (3), (4). Based on this treatment a further extension is then developed, including the influence due to imperfect reflection at the valve end. Four different bases for the specification of the amount of reflection realized are presented and the treatment is developed to include any of these according to choice. These four methods are as follows: (1) A constant fraction or percentage of complete reflection. (2) A fraction or percentage of complete reflection defined as (ata)/ar where aI = area of full valve opening and a = area of opening at any instant during valve movement. (3) A fraction or percentage of complete reflection defined as (A-a)/A where A = cross-section area of pipe and a = area of valve opening at any instant during valve movement. (4) A fraction or percentage of complete reflection defined as (vv)/VI where for closure v, = full initial velocity and for opening vl = full final velocity, while v = velocity at any instant during valve movement. The treatment throughout the paper includes both closure and opening of the valve, either in whole or in part, or in general any amount of valve movement either in closure or opening. The paper is illustrated with diagrams shlowing typical numerical cases. Of the various conditions thus brought within the scope of a form of analytical treatment, the author considers that part of the paper relating to No. 5 of more especial interest, representing, so far as he is aware, a distinct extension of earlier treatments of the problem and in such manner as to bring under some form of analytical control an important condition which must always prevail in actual cases of the development of shock or water ram in liquid conduits.